Based on the type of equations in the system, what is the greatest possible number of solutions (x2+y2=9/9x+2y=16?
2 answers:
Answer:
`Option B.
Step-by-step explanation:
The given system of equations is
The graph of first equation is circle and the graph of second equation is a line.
We know that a line can intersect a circle at most 2 times. So, the greatest possible number of solutions is 2.
First equation can be rewritten as
It is the standard form of a circle , where (h,k) is center and r is radius.
In the above equation h=0,k=0 and r=3. It is a circle with radius 3 and centered at origin.
The second equation is
It is a linear equation.
Table of values.
x y
0 8
1 3.5
2 -1
Plot these points on a coordinate plane and connect them by a straight line.
From the below graph it is clear that the line and circle intersect each other at two points. So, the given system of equation have two solutions.
Therefore, the correct option is B.
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Answer:
P = 57°
Step-by-step explanation:
Given the following :
PQ = 17
QR = 15
PR = 14
Using the cosine formula since the length of the three sides are given:
a2 = b2 + c2 – 2bccos(A)
To find P:
QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)
15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)
225 = 289 + 196 - 476 cosP
476*CosP = 485 - 225
476*CosP = 260
CosP = 260/476
CosP = 0.5462184
P = Cos^-1(0.5462184)
P = 56.892029
P = 57°
Answer:
Points -2 and -6 on the number line are the two solutions.
Step-by-step explanation:
Use the definition of absolute value as a starting point
To solve the equation, you need to treat the two cases as above:
The solution x=-2 is consistent with the condition x>=-4, so it is the first and valid solution. Now the second case of the absolute value:
Again, the second solution -6 complies with the requirement that x<-4, so it is valid.